It is understood that Chelsea have compiled a wish-list of possible replacements, with former Barcelona coach Luis Enrique at the top of it, although they deny opening talks with any potential candidate, says the London Evening Standard.
But when asked if he remains confident about staying at Chelsea, he replied: "Yes. I'm not thinking for only one moment to go away from this club - my commitment is totally for this club.
“We are trying to do our best. You know that a lot of time the manager (future) depends on results. In this case we are having poor results. For this reason we must pay great attention.
“In every situation we have to divide the responsibility, when it is a positive or negative situation. When you have this period with so many poor results, you have to divide responsibility with me, the players and the club."
Despite Chelsea's struggles in recent months, the majority of the club's supporters continue to support Conte and sing his name during matches.
“For sure I have to say thanks to the fans," Conte said. “From the start of my experience at Chelsea, they have tried to stay behind me in every game, they continue to do this and I'm proud about this. They understand I'm giving all of myself and maybe more. They deserve the best."